1115 Counting Nodes in a BST (30 分)

1115 Counting Nodes in a BST (30 分)

 

A Binary Search Tree (BST) is recursively defined as a binary tree which has the following properties:

• The left subtree of a node contains only nodes with keys less than or equal to the node's key.
• The right subtree of a node contains only nodes with keys greater than the node's key.
• Both the left and right subtrees must also be binary search trees.

Insert a sequence of numbers into an initially empty binary search tree. Then you are supposed to count the total number of nodes in the lowest 2 levels of the resulting tree.

Input Specification:

Each input file contains one test case. For each case, the first line gives a positive integer N (≤) which is the size of the input sequence. Then given in the next line are the N integers in [ which are supposed to be inserted into an initially empty binary search tree.

Output Specification:

For each case, print in one line the numbers of nodes in the lowest 2 levels of the resulting tree in the format:

n1 + n2 = n

where n1 is the number of nodes in the lowest level, n2 is that of the level above, and n is the sum.

Sample Input:

9
25 30 42 16 20 20 35 -5 28

Sample Output:

2 + 4 = 6


就是一个建树的问题，不值30分

#include <bits/stdc++.h>
using namespace std;
struct Node{
    int val;
    Node *left, *right;
};
int n, x, vis[2000];
int maxl = 0;
Node *build(Node *root, int val){
    if(root == NULL){
        root = new Node();
        root->val = val;
        root->left = root->right = NULL;
    }else{
        if(val <= root->val){
            root->left = build(root->left, val);
        }else{
            root->right = build(root->right, val);
        }
    }
    return root;
}
void output(Node *root, int x){
    if(root != NULL){
        vis[x]++;
        maxl = max(maxl,x);
        output(root->left, x+1);
        output(root->right, x+1);
    }
}
int main(){
    cin >> n;
    Node *tree = NULL;
    for(int i = 0; i < n; i++){
        cin >> x;
        tree = build(tree,x);
    }
    output(tree, 1);
    cout << vis[maxl] <<" + "<<vis[maxl-1]<<" = "<<vis[maxl]+vis[maxl-1]<<endl;
    return 0;
}